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Approximation of functions 1 - NMNV543

Title:	Aproximace funkcí 1
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://numapprox.blogspot.cz

Guarantor:	doc. RNDr. Petr Tichý, Ph.D.
Class:	M Mgr. NVM M Mgr. NVM > Povinně volitelné
Classification:	Mathematics > Numerical Analysis
Incompatibility :	NNUM011
Interchangeability :	NNUM011
Is interchangeable with:	NNUM011

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Annotation -

Last update: doc. RNDr. Václav Kučera, Ph.D. (05.12.2018)

Introduction to approximation theory of continuous functions in normed linear spaces, with an emphasis on numerical methods for the computation of approximations. The course deals with problems of polynomial interpolation, minimax approximation, and least squares approximation. Students will test the algorithms practically during the exercise.

Course completion requirements -

Last update: doc. RNDr. Petr Tichý, Ph.D. (06.10.2017)

It is not necessary to obtain a course-credit before passing the exam.

The course-credit will be granted for the attendance and for a short presentation given during the semester.

The nature of these requirements does not allow a possibility of some additional attempts to obtain the course-credit.

Literature -

Last update: doc. RNDr. Václav Kučera, Ph.D. (29.10.2019)

M. J. D. Powell, Approximation theory and methods. Cambridge University Press, Cambridge-New York, 1981.

N. L. Trefethen, Approximation Theory and Approximation Practice. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2013.

E. W. Cheney, Introduction to approximation theory. AMS Chelsea Publishing, Providence, RI, 1982.

R. A. DeVore, G. G. Lorentz, Constructive Approximation, vol. 303 of Grundlehren der Mathematischen Wissenschaften,, Springer-Verlag, Berlin, 1993.

Requirements to the exam -

Last update: doc. RNDr. Petr Tichý, Ph.D. (06.10.2017)

The exam is oral. Requirements for the oral exam correspond to the syllabus of the course, presented at the lectures.

Syllabus -

Last update: doc. RNDr. Václav Kučera, Ph.D. (05.12.2018)

Best approximation in normed linear spaces, approximation operators. Polynomial approximation: Barycentric interpolation formula, Chebyshev interpolant and projection. Minimax approximation, Haar condition, Remez algorithm. Least squares approximation, orthogonal polynomials, periodic functions, uniform convergence, Jackson's theorems. Practical applications: Chebfun, spectral methods, matrix functions.

Entry requirements -

Last update: doc. RNDr. Petr Tichý, Ph.D. (02.05.2018)

Fundamentals of mathematical analysis and numerical linear algebra. Basic knowledge of the Matlab programming language.